Simple Interest
Math MCQs

Question :    How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?

Correct Answer  $7200

Solution & Explanation

Solution

Given,

Amount (A) = $8640

Rate of Simple Interest (R) = 4%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$8640 = P (1 + 4% × 5)

⇒ $8640 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8640 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8640 = P (1 + ²⁰/₁₀₀)

⇒ $8640 = P (^{100 + 20}/₁₀₀)

⇒ $8640 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8640

⇒ P = ⁸⁶⁴⁰/_¹²⁰/100

⇒ P = 8640 × ¹⁰⁰/₁₂₀

⇒ P = ^{8640 × 100}/₁₂₀

⇒ P = ⁸⁶⁴⁰⁰⁰/₁₂₀

⇒ P = $7200

Thus, the sum borrowed (P) = $7200 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8640, then the Principal = ¹⁰⁰/₁₂₀ × 8640

= ^{100 × 8640}/₁₂₀

= ⁸⁶⁴⁰⁰⁰/₁₂₀

= 7200

Thus, Principal = $7200

Thus, the sum borrowed = $7200 Answer

Similar Questions

(1) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.

(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.

(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.